The recession factor reduces the rate at which the
quanta reach the observer because it dilutes the stream
of quanta. The effect is quite simple, and may be
described in the following way. Suppose that, in one
second of time, a stationary nebula radiates a certain
number of quanta n in the direction of the, observer.
Since all of the quanta travel with the velocity of light,
c miles per second, the first of the quanta to leave the
nebula had travelled forward the distance c = 186, 000
miles, when the last of the n quanta leaves the nebula.
Thus the n quanta which leave the nebula during one
second are scattered uniformly over a path whose
length is c.

Now suppose that the nebula is receding from the
observer with a velocity of v miles per second. It still
radiates the same number of quanta in one second of
time, namely n, but during the interval between the
emission of the first and the last of these quanta the
first quantum has travelled forward the distance c while
the nebula has receded the distance v. Thus the n
quanta from the receding nebula are distributed over
the path c + v, while the same number of quanta from
the stationary nebula are distributed over the path c.
Evidently, the recession has increased the separation
between successive quanta by the factor
(c + v) / c = 1 + v / c. The dilution
of the stream of quanta necessarily reduces their
rate of arrival and, consequently,
the apparent luminosity of the nebula. The recession
factor 1 + v/c must be applied to a receding nebula,
in addition to the energy factor; the observer receives
fewer quanta and each of the quanta has lost energy.

In practice, the expression 1 + v / c is generally
replaced by
1 + d /
, because the use of
the factor implies
an expanding universe, and current theories of such a
universe regard the second expression as the proper
formulation. This procedure is followed in the present discussion.

The recession effect, unlike the energy effect, is not
selective; it is not distorted by the atmosphere, the
telescope, or the photographic film. Consequently, the
recession factor, in its simple form
1 + d /
, may be
applied to apparent luminosities on any system, photographic as well as
bolometric. The fractional reduction
in luminosity is merely the fractional red-shift. In
technical terms apparent magnitudes are increased by the increment

The effect of recession is quite negligible for ordinary
velocities (or red-shifts) ; for instance, a velocity of
1,860 miles per second (red-shift = 0.01) reduces the
apparent luminosity by only 1 per cent. But at great
distances, where red-shifts are large, the effects are
measurable quantities. For the largest shifts recorded
with the spectrograph the reduction is about 14 per
cent.; at the limit of the deepest accurate survey, the
estimated reduction is about 23 per cent.

It is evident that critical tests of the interpretation
of red-shifts as velocity-shifts could be readily made,
provided we had reliable distance-criteria which were
independent of apparent luminosity. But in the absence
of such criteria we must return to the method of
parallel hypotheses, and examine the general features of
the observable region on the basis of alternative scales of distance.